Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi” Ph.D thesis of: Yasser Gritli Ph.D. in Electrical Engineering XXVI Cycle Power Electronics, Electrical Machines and Drives (ING-IND/32) Diagnosis and Fault Detection in Electrical Machines and Drives based on Advanced Signal Processing Techniques Tutor : Prof. Fiorenzo Filippetti Final dissertation on March 2014 Ph.D. Coordinator: Prof. Domenico Casadei
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Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi”
Ph.D thesis of:
Yasser Gritli
Ph.D. in Electrical Engineering XXVI Cycle
Power Electronics, Electrical Machines and Drives (ING-IND/32)
Diagnosis and Fault Detection in Electrical Machines and Drives
based on Advanced Signal Processing Techniques
Tutor :
Prof. Fiorenzo Filippetti
Final dissertation on March 2014
Ph.D. Coordinator:
Prof. Domenico Casadei
AKNOWLEDGEMENTS
This research project has been carried out at the Department of Electrical, Electronics and
Information Engineering “Guglielmo Marconi” (DEI), at University of Bologna, Bologna,
ITALY.
First of all, I would like to express my deep and sincere gratitude to my supervisor Prof.
Fiorenzo Filippetti for his excellent supervision and helps during this work. I would like to
thank all my Professors at the Department of Electrical Engineering for all their technical,
professional and administrative support.
I want in special thanks to, Prof. Domenico Casadei, Prof. Giovanni Serra, Prof. Claudio
Rossi, Prof. Luca Zarri, Prof. Gabriele Grandi, and Prof. Angelo Tani.
My greatest thanks go to Prof. Rosario Miceli from University of Palermo-Italy, Prof. Sang
Bin Lee from University of Seoul-Korea, Prof. Gérard-André Capolino from University of
Picardie “J. Verne”- France, and Prof. Mohamed Ben Rejeb from University of Tunis El
Manar-Tunisia.
Many thanks go also to all my colleagues, who have assisted me during the work of this
Ph.D. thesis especially Andrea Stefani, Michele Mengoni, Matteo Marano, and Alessio
Pilati.
Finally, I owe my gratitude to my Mother, my Father, my Sisters, my Boutheina, my Sarra
and my family members for all their love and support.
i
CONTENT
Content ..................................................................................................................................................... i Liste of figures ...................................................................................................................................... iv
List of tables ........................................................................................................................................... x
Nomenclature ........................................................................................................................................ xi Preface .................................................................................................................................................... 1 Chapter 1 : State of art in diagnostic for electrical machines ............................................ 4 1.1 Introduction .............................................................................................................................. 5 1.2 Stator related-faults .................................................................................................................. 6
4.3 Analysis of rotor fault in double cage induction machine ............................................ 76 4.3.1 Motor Current Signature Analysis .............................................................................. 78
4.3.1.1 System description ............................................................................................. 78 4.3.1.2 Results .................................................................................................................. 78
Failure of outer cage bars tends to spread to neighboring bars as the currents of the
damaged bars are distributed into them. This could eventually result in startup failure
due to insufficient startup torque [23]. An example of a DCIM failure with outer cage
bar damage is shown in Fig. 1.5. This 800 kW, 3.3kV pulp stirrer motor recently failed
in a paper mill in Korea. The inner cage was in good condition. On the contrary, the
excessive thermal and thermo-mechanical stress due to outer cage damage resulted in
“melting” and “fracture” of the outer bars (the temperature exceeded 200°C) [22]. This
produced copper bar fragments that caused stator end winding insulation and core
damage, and led to irreversible motor failure.
For wound-rotor machines, the physics of rotor fault is similar to stator fault and it
results either in an increase of rotor resistance or in short and open circuits. In case of
increased resistance, the machine can operate also after the fault occurrence, while in
case of short and open circuits, after fault operation is limited to a short time. For wound
rotor machines it is reasonable to assume that the percentage of stator windings and
rotor windings faults can be divided in equal parts. In fact the rotor circuits of wound
motors are usually poorly protected even in presence of adjunctive components (slip-
ring connections, resistors connected to the slip rings).
Cage50%
Shaft20%
Magnetic circuit20%
Others 10%
11
(a) (b)
Fig. 1. 5 Example of 3.3 kV, 800kW double cage induction motor failure due to outer cage damage: (a) outer bar damage, (b) stator end-winding insulation
failure due to broken copper fragments from outer bar
1.3.2 Rotor fault components propagation
An electrical machine is subject to both electromagnetic and mechanical forces
which are symmetrically distributed. In healthy conditions, the equivalent windings
impedances are identical and consequently the stator and rotor currents are balanced.
Under these normal conditions, only normal frequency components at f and sf exist
respectively on stator and rotor currents, where f is the power grid frequency and s the
slip.
If the rotor is damaged, the rotor symmetry of the machine is lost, the equivalent
rotor windings impedances are no longer equal, and a reverse rotating magnetic field is
produced. Consequently, an inverse frequency component appears in the rotor current at
the frequency −sf. This component produces a fault frequency (1−2s)f in the stator
currents which causes a pulsating torque and a speed oscillation at the frequency 2sf.
This frequency induces both a reaction current at frequency (1−2s)f and a new
component at frequency (1+2s)f. The last frequency produces new components in the
stator currents at frequencies ±3sf. As a consequence, a set of new frequency
components defined as (1.3) appear in the spectrum of stator currents and a set of new
frequency components expressed as (1.4) appear in spectra of rotor currents [15], [16].
0,1,2,...
1 2ksr kf ks f
(1. 3)
12
0,1,2,...
1 2krr kf k sf
(1. 4)
Usually, the diagnostic techniques are focused on the detection of fault dominant
frequency components in stator signals at the frequency (1±2s)f and at the frequency −sf
in rotor signals. Fig. 1.6 shows the rotor fault propagation in frequency and in time. This
fault can be monitored and detected in a variety of methods. In fact, the equivalent
parameters of the machine are changed, the currents are not balanced, and all the
quantities linked to the currents are affected by the faults. The choice of the best method
for a specific application can be made according to the following priorities: simplicity,
sensitivity, ruggedness and reliability. Moreover, in closed-loop operation the control
system ensures a safe operation even under an unbalance in both stator and rotor
windings. Consequently, the typical rotor current fault frequency components is reduced
by the compensating action of the control system. However, under these conditions the
fault-related frequencies are reflected in the voltages that can be used for fault detection
[24].
Fig. 1.6 Frequency domain propagation of a rotor fault. The minus sign (–) identifies current inverse sequence components
1.4 Signal processing techniques for electrical machines
diagnosis
Fault detection is efficient only when fault evolution is characterized by a time constant
of the order of days or greater, so that suitable action can take place. In any case, a key
item for the detection of any fault is proper signal conditioning and processing. With
13
advances in digital technology over the last few years, adequate data processing
capability is now available on cost-effective hardware platforms. They can be used to
enhance the features of diagnostic systems on a real-time basis in addition to the normal
machine protection functions.
Fig. 1.7 Block topology of signal-based diagnostic procedure
Signal-based diagnosis looks for the known fault signatures in quantities sampled from
the actual machine. Then, the signatures are monitored by suitable signal processing
(Fig. 1.7). Typically, frequency analysis is used, although advanced methods and/or
decision-making techniques can be of interest. Here, signal processing plays a crucial
role as it can be used to enhance signal-to-noise ratio and to normalize data in order to
isolate the fault from other phenomena and to decrease the sensitivity to operating
conditions.
Different diagnosis techniques for electrical machines can be found in literature. In the
category of time-domain analysis technique there are: the time-series averaging method,
which consist in extracting a periodic component of interest from a noisy compound
signal, the signal enveloping method, and the Kurtosis method, and the spike energy
method [6], [25]-[28].
In [26], the oscillation of the electric power in the time domain becomes mapped in a
discrete waveform in an angular domain. Data-clustering techniques are used to extract
an averaged pattern that serves as the mechanical imbalance indicator. The maximum
covariance method is another technique that is based on the computation of the
covariance between the signal and the reference tones in the time domain [27].
Spectral frequency estimation techniques were widely adopted in machine diagnosis, as
frequency domain tool analysis. These approaches are based on the Fourier analysis
(FA) for investigating the signals being analyzed. Unluckily, electrical machines operate
mostly in time-varying conditions. In this context, slip and speed vary unpredictably,
and the classical application of FA for processing the voltage set points or the measured
currents fails, as shown in [29]–[31]. In fact, the bandwidth of the fault frequency
components is related to the speed variation. Among different solutions, the signal
demodulation [29], the high-resolution frequency estimation [32], and the discrete
14
polynomial-phase transform [33] have been developed to reduce the effect of the non-
periodicity of the analyzed signals or to detect multiple faults [34]. These FA-based
techniques give high-quality discrimination between healthy and faulty conditions, but
they cannot provide any time-domain information.
This shortcoming in the FA-based techniques can be reduced by analyzing a small
interval of the signal by means of the short-time Fourier transform. This method has
been widely used to detect both stator and rotor failures in electrical motors. However,
the fixed width of the window and the high computational cost required to obtain a good
resolution still remain major drawbacks of this technique [35]–[37]. Based on the
instantaneous frequencies issued from the intrinsic mode functions, the Hilbert–Huang
transform was proposed for motor diagnosis and has shown quite interesting
performances in terms of fault severity evaluation [38]–[41]. Other quadratic transforms,
such as the Wigner–Ville distribution (WVD), suffer from the same constraint [42]. This
limitation can be overcome by new advanced time–frequency distributions such as
smoothed pseudo-WVDs [42], Choi–Williams distribution [42], [43], and Zhao–Atlas–
Marks distribution [44]. However, the removal of cross-terms leads generally to
reducing the joint time–frequency resolution and the signal energy.
Being a linear decomposition, wavelet transform (WT) provides a good resolution in
time for high-frequency components of a signal and a good resolution in frequency for
low-frequency components. In this sense, wavelets have a window that is automatically
adjusted to give the appropriate resolution developed by its approximation and detail
signals. Motivated by the aforementioned proprieties, in recent years, some authors have
pointed out the effectiveness of WT for tracking fault frequency components under non-
stationary conditions. WT was used with different approaches for monitoring motors.
The related techniques are the undecimated discrete WT [45], the wavelet ridge method
[46], the wavelet coefficients analysis [47], [48], or the direct use of wavelet signals
[48]–[50] for stator- and rotor-fault detection. Recently, fractional Fourier transform has
been proposed in [51], providing an innovative graphical representation of rotor-fault
components issued from discrete WT in the time–frequency domain. More intensive
research efforts have been focused on the usage of both approximation and detail signals
for tracking different failure modes in motors, such as broken bars [35], [49]- [50], [52]-
[53] interturn short circuits [35], [51], [54], mixed eccentricity, [49], [52], [55], and
increasing resistance in a stator phase [15], [45], [56] or in a rotor phase [15], [37], [57].
Most of the reported contributions are based on wavelet analysis of currents during the
start-up phase or during any load variation. In this context, the frequency components
are spread in a wide bandwidth as the slip and the speed change considerably. The
situation is more complex under rotor-fault conditions due to the proximity of the fault
components to the fundamental frequency. These facts justify the usage of multidetail
15
or/and approximation signals resulting from the wavelet decomposition [35], [48]–[50],
[52]. Moreover, the different decomposition levels are imposed by the sampling
frequency. However, the dependence on the choice of the sampling frequency and on
the capability of tracking multiplefault frequency components makes difficult to
interpret the fault pattern coming from wavelet signals and increases the diagnosis
complexity. Moreover, the usage of large frequency bandwidths exposes the detection
procedure to erroneous interpretations due to a possible confusion with other frequencies
related to gearbox or bearing damages [58].
In order to quantify the fault severity, the energy of approximation and/or detail signals
resulting from wavelet decomposition has been already used [35], [49]. However, this
attempt reduces each time–frequency band to a single value. In this way, the time-
domain information could be lost.
1.5 Conclusion
Potential failure modes in electrical machines, as stator and rotor electrical/mechanical
faults, which are investigated in this thesis, were exhaustively analyzed. A literature
review of the corresponding diagnosis techniques were also presented.
Finally, an important issue deduced particularly from section (1.4), which is the need to
develop new diagnostic approaches for electrical machines operating in time-varying
conditions, with possible improvements that can be formulated as follows:
1) Capability of monitoring the fault evolution continuously over time under any transient operating condition;
2) No requirement for speed/slip measurement or estimation;
3) Higher accuracy in filtering frequency components around the fundamental;
4) Reduction in the likelihood of false indications by avoiding confusion with other fault harmonics (the contribution of the most relevant fault frequency components under speed-varying conditions are clamped in a single frequency band);
5) Low memory requirement due to low sampling frequency;
6) Reduction in the latency of time processing (no requirement of repeated sampling operation).
Effectively, in the present thesis, an effective method to solve the aforementioned open points in time-varying conditions is presented. A complete description which systematizes the use of the developed approach is presented in Chapter 2, and experimental results showing the validity of the presented technique are presented and exhaustively commented in the next chapters.
16
REFERENCES
[1] A.H. Bonnet, and G.C. Soukup, ‘‘Cause and analysis of stator and rotor failures
in three-phase squirrel cage induction motors,” IEEE Transactions on Industry
As previously introduced, stator or rotor faults in wound rotor induction machines can
be detected by tracking the evolution of the fault components fkrs or fkrr, respectively
from rotor variables (currents, voltages). Under speed-varying conditions, fault
frequency components are spread in a frequency band [flow , fup] related to the speed,
where flow and fup denote the lower and upper limits of the fault frequency evolution
respectively. A simple processing of the currents or to control variables allows shifting
the fault component at frequency fkrs or fkrr in a dedicated frequency band among those
shown in Table 2.2. More in detail, a frequency sliding equal to ,krs krrslif is applied to the
rotor variables (currents, voltages) by using (2.7), so that each single fault frequency
component is shifted into a prefixed single frequency band.
,2, ,( ) Re ( )krs krr
slif tkrs krr krs krrslx t x t e (2.7)
37
where ,krs krrx is the rotor current or voltage space vector, to be analyzed. Then, the
discrete WT is applied to the resulting signal ,krs krrslx to extract the fault signature in the
frequency band that has been chosen.
As illustrated by Fig. 2.10, the DWT divides the frequency content of the original
signal into logarithmically spaced frequency bands. The approximation aJ and detail dJ
have the same frequency bandwidth, equal to fsam/2J+1. Thanks to its proximity to 0 Hz,
the approximation aJ is less subject to overlapping effect than detail signals and hence is
more suitable for fault analysis [23], [26]. Consequently, the frequency bands
]2,0[ )1(sam
J f are chosen to track the main fault components.
an
dn
dn-1
d1
[0:fs/2n+1] [f
s/2n+1:f
s/2n] [f
s/2n:f
s/2n-1] [f
s/22:f
s/2]
Freq. (Hz)
Fig. 2. 10 The DWT filtering process for decomposition of signal into predetermined frequency bands
Being related to the sampling frequency fsam, the level J of decomposition has to be
chosen in such a way to satisfy the following criterion:
( 1)2 Jup low samf f f (2.8)
Condition (2.8) means that the size of the frequency bandwidth in which the fault
frequency component evolves should be smaller than the bandwidth related to the
approximation signal aJ. Since flow and fup may be affected by uncertainties due to speed
ripples or noise, it is convenient to introduce a tolerance factor , slightly greater than
one, to avoid false alarms after the fault quantification process.
Thus, the level of decomposition is chosen in order to satisfy the following constraint:
log /1
log(2)
sam up lowf f fJ
(2.9)
Once the decomposition level has been chosen, the value of the sliding frequency fsli can
be computed as follows:
12 / 2J
sli low up samf f f f (2.10)
38
With regard to the type of mother wavelet, the use of a low-order Daubechies mother
wavelet (db10) has already provided satisfactory results.
Recently, a high order mother wavelet has been recommended to minimize the
overlapping effect between adjacent frequency bandwidths, and it has already been
tested for rotor broken bars detection [24], [26]. Several types of mother wavelets such
as Daubechies, Coiflet, and Symlet have been tested. Regardless of different properties,
the qualitative analysis of the results has shown that no significant advantages appeared
[27]. The 40th order Daubechies mother wavelet (db40) was adopted in order to
minimize the overlapping effect between adjacent frequency bands related to detail d8
and approximation a8.
Once the state of the machine has been diagnosed, a quantitative evaluation of the fault
degree is necessary. For this purpose, the fault indicator mPaj at different resolution
levels j has been introduced:
2
1
1( , ) ( )
n
j jn
mPa I V a nn
(2.11)
where aj(n) is the approximation signal of interest, Δn denotes the number of samples and j the decomposition level.
The fault indicator is periodically calculated over time, every n sampling period and
over a time interval including the latter n samples. This process is shown in Fig. 2.11.
The values of n and n were chosen according to the desired time sensitivity needed to observe the fault evolution. When the fault occurs, the signal energy distribution changes due to the presence of the fault frequency component. Hence, the energy excess confined in the approximation signal may be considered as a fault indicator in case of stator or rotor unbalances.
''a
j''
sign
al
Time
Samples
n
n
TIN=1
TIN=2
TIN=3
''a
j''
sig
na
lse
qu
en
ces
Fig. 2. 11 Principle of time interval calculation as a function of the Time Interval Number (TIN)
39
2.5 Conclusion
The problematic of signal processing techniques used for electrical machine diagnosis
operating in time-varying conditions was firstly analyzed in this chapter. Then, a new
effective method is completely described and systematized in order to achieve the
different open points established in the previous chapter providing:
- Capability of monitoring the fault evolution continuously over time under any
transient operating condition;
- Speed/slip measurement or estimation is not required;
- Higher accuracy in filtering frequency components around the fundamental;
- Reduction in the likelihood of false indications by avoiding confusion with other
fault harmonics (the contribution of the most relevant fault frequency components
under speed-varying conditions are clamped in a single frequency band);
- Low memory requirement due to low sampling frequency;
- Reduction in the latency of time processing (no requirement of repeated sampling
operation).
40
REFERENCES
[1] T. Chow and S. Hai, "Induction machine fault diagnostic analysis using wavelet
[27] J. Antonino-Daviu, M. Riera-Guasp, J. Roger-Folch, F. Martínez-Giménez, A.
Peris, “Application and optimization of the discrete wavelet transform for the
detection of broken rotor bars in induction machines,” Appl. Comp. Harmon.
Anal., vol. 21, no. 2, pp. 268–279, Sep. 2006.
43
44
CHAPTER 3 : ANALYSIS OF STATOR
AND ROTOR FAULTS IN WOUND
ROTOR INDUCTION MACHINES
3.1 Introduction ........................................................................................................................... 45 3.2 System description ................................................................................................................ 45
3.2.1 WRIM Control system ................................................................................................. 45 3.2.2 Experimental system ..................................................................................................... 49
4.3 Analysis of rotor fault in double cage induction machine ............................................ 76 4.3.1 Motor Current Signature Analysis .............................................................................. 78
4.3.1.1 System description ............................................................................................. 78 4.3.1.2 Results .................................................................................................................. 78
4.3.2 Motor Vibration Signature Analysis ........................................................................... 83 4.3.2.1 System description ............................................................................................. 84 4.3.2.2 Results .................................................................................................................. 85
In this chapter, the proposed diagnosis technique is validated for the detection of
rotor broken bars in squirrel cage induction motors. The diagnosis of rotor faults in
induction machine is commonly carried out by means of Motor Current Signature
Analysis (MCSA), i.e., by classical spectrum analysis of the input currents. However
MCSA has some drawbacks that are still under investigation. The main concern is that
an efficient frequency transformation cannot be made for induction machines
operating in speed–varying condition, since slip and speed vary and so does the
sideband frequencies.
Another important issue related to double squirrel cage induction motors (DCIMs),
subject to higher misdetection of outer cage damage in time-varying load applications,
such as conveyor belts, pulverizers, etc., for which DCIMs are frequently employed.
This is because the magnitude of the rotor fault frequency components (RFFCs) in the
current spectrum of faulty DCIMs are small due to the low magnitude current
circulation in the outer cage under steady state operation. In case of load variation, the
small RFFCs are spread in a bandwidth proportional to the speed variation, which
makes them even more difficult to detect.
In this chapter, the proposed diagnosis technique is firstly applied for rotor broken
bars detection for single cage induction machine, by investigating MCSA. The second
part of this chapter is focused on the detection of rotor outer cage bar faults for double
cage motors. An experimental study on a custom-built fabricated Cu double cage rotor
induction motor shows that the proposed diagnosis technique can provide improved
detection of outer cage faults particularly used in time-varying load applications.
Experimental results show the validity of the developed approach, leading to an
effective diagnosis method for broken bars in induction machines.
4.2 Analysis of rotor fault in single cage induction machine
4.2.1 System description
In order to validate the results obtained in simulations a test bed was realized. A 7.5
kW, 2 poles pair induction machine was used (Table. 4.1). Two rotors are available, one
healthy and one with a drilled rotor bar. The induction machine is coupled to a 9kW
separately excited DC machine controlled in speed. This allows to reproduce the
simulated speed transients. Photos of the experimental test bed are shown in Fig. 4.1.
Machine currents and speed are sampled at 3.2 kHz with a time duration of 10 seconds.
A smaller number of points could be used without affecting the performances of the
proposed procedure.
70
Table. 4. 1 Single Cage Induction Motor parameters
Parameter Unit Value
Rated power kW 7.5
Rated stator voltage V 380
Nominal stator current A 15.3
Rated frequency Hz 50
Rated speed rpm 1440
Stator phase resistance Ω 0.54
Rotor phase resistance Ω 0.58
Stator inductance mH 88.4
Rotor inductance mH 83.3
Magnetizing inductance mH 81.7
Pole pairs 2
Number of rotor bars 28
Fig. 4. 1 Test bed photo (left). The faulty rotor with one drilled rotor bar (right)
4.2.2 Results
4.2.2.1 Fault detection under speed-varying conditions
The induction motor has been initially tested in healthy conditions during a prefixed
transient from 1496 rpm to 1460 rpm, corresponding to slip ranges from s=0.002 to
s=0.026. Another test, for the same speed transient was made with the machine
operating with one rotor broken bar. The instantaneous values of speed and phase
currents, corresponding to the healthy and faulty cases, are depicted in Fig. 4.2 (a-b) and
71
Fig. 4.2 (c-d) respectively. For the considered speed range, approximation a9 was chosen
for extracting the contribution of the fault components (1-2s)f and (1+2s)f .Therefore the
choice of fsl is made to shift these fault components inside the frequency interval [0,
3.125] Hz corresponding to approximation. For the sake of clarity only the a9 signal will
be reported. In healthy condition, the 9th approximation signal a9, resulting from the
wavelet decomposition of the stator phase current, does not show any kind of variation
(Fig. 4.3). This indicates the absence of the fault component (1-2s)f, leading to diagnose
the healthy condition of the motor under speed-varying condition.
Fig. 4. 2 Instantaneous values of a-b) speed and c-d) stator phase currents under healthy and one
rotor broken bar respectively
However, in faulty condition (one rotor broken bar) approximation a9 shows significant
variation in magnitude observed in Fig. 4.4. During the first time period (t=0s to t=2s),
under a constant speed of 1496 rpm, the 9th approximation signal, representative of the
(1-2s)f frequency component, do not show any important variations. This is due to the
fact that at low load level (under 4% of the nominal torque) the fault frequencies are
practically superimposed to the fundamental and magnitudes are not detectable. During
deceleration (around t=2s), a9 shows particular magnitude escalation proportional to the
abrupt deceleration until reaching a quasi steady-state magnitude (under 66% of the
nominal torque).
0 2 4 6 8 101450
1460
1470
1480
1490
1500
1510- a -
Time (s)
Sp
eed
(rp
m)
0 2 4 6 8 101450
1460
1470
1480
1490
1500
1510- b -
Time (s)
Sp
eed
(rp
m)
0 2 4 6 8 10
-20
-10
0
10
20
- c -
Time (s)
Cu
rre
nt
(A)
0 2 4 6 8 10
-20
-10
0
10
20
- d -
Time (s)
Cu
rre
nt
(A)
72
More in detail, the oscillations observed in the signal a9, with quasi-constant amplitude,
follow a characteristic pattern that fits the evolution in frequency of the fault component
(1-2s)f, during the speed transient.
The second rotor fault signature tracked is related to the fault component at frequency
(1+2s)f. The corresponding experimental results, under healthy and rotor broken bar are
presented in Fig. 4.5 and Fig. 4.6. The same observations as for the signature of the side
band (1-2s)f under the considered rotor unbalance, are reached; the comparison of the
approximation signal a9, issued from wavelet decomposition of the stator phase current,
under healthy (Fig. 4.5-b) and rotor broken bar (Fig. 4.6-b) reproduce clearly the
magnitude evolution of the fault component (1+2s)f dynamically over time.
If we confine our attention on the approximation signal a9 depicted in Fig. 4.4-b and Fig.
4.6-b, we can notice that the rotor fault signature issued from the fault component (1-2s)f
is more relevant than the corresponding one related to the (1+2s)f component. This is
mainly due to the the machine-load inertia effect on high order rotor fault harmonics.
The 9th approximation signal obtained from the experimental results shows the
sensitivity and the effectiveness of this particular signal a9 to reproduce the contribution
of the frequency components (1-2s)f and (1+2s)f under large speed varying conditions.
Fig. 4. 3 DWT analysis of stator phase current under speed-varying condition, for tracking the
fault component (1-2s)f ; Healthy condition
0 1 2 3 4 5 6 7 8 9 10
-20
-10
0
10
20
- a -
Time (s)
Cu
rre
nt
(A)
0 1 2 3 4 5 6 7 8 9 10-1.2
-0.8
-0.4
0
0.4
0.8
1.2- b -
Time (s)
a9
73
Fig. 4. 4 DWT analysis of stator phase current under speed-varying condition, for tracking the
fault component (1-2s)f ; One Broken Bar
Fig. 4. 5 DWT analysis of stator phase current under speed-varying condition, for tracking the
fault component (1+2s)f ; Healthy condition
0 1 2 3 4 5 6 7 8 9 10
-20
-10
0
10
20
- a -
Time (s)
Cu
rren
t (A
)
0 1 2 3 4 5 6 7 8 9 10-1.2
-0.8
-0.4
0
0.4
0.8
1.2- b -
Time (s)
a9
0 1 2 3 4 5 6 7 8 9 10
-20
-10
0
10
20
- a -
Time (s)
Cu
rren
t (A
)
0 1 2 3 4 5 6 7 8 9 10-1.2
-0.8
-0.4
0
0.4
0.8
1.2- b -
Time (s)
a9
74
Fig. 4. 6 DWT analysis of stator phase current under speed-varying condition, for tracking the
fault component (1+2s)f ; One Broken Bar
4.2.2.2 Fault quantification
Once the machine is qualitatively diagnosed, the fault indicator based on a cyclic mean
power calculation of the approximation a9, resulting from the wavelet decomposition
applied to one stator current, has been processed to evaluate quantitatively the degree
of the fault extent.
The cyclic evolution of the fault indicator mPa9, representative of the contributions of
the fault components components (1-2s)f and (1+2s)f , issued from the experimental
tests (Figs. 4.3-4.6), under healthy and rotor broken bar conditions are depicted in Fig.
4.7 and Fig. 4.8 respectively. In healthy condition, and under large range of speed
variations, mPa9 does not show any significant change. Consequently, the indicator
values for the healthy motor are considered as a baseline to set the threshold for
discriminating healthy from faulty conditions. Under rotor broken bar condition the
calculated mPa9 indicator shows a noteworthy increase. The large energy deviation
observed in faulty condition proves the effectiveness of the proposed approach, since
the transient speed motor operation does not disturb the fault assessment, in
comparison with the healthy case.
0 1 2 3 4 5 6 7 8 9 10
-20
-10
0
10
20
- a -
Time (s)
Cu
rre
nt (A
)
0 1 2 3 4 5 6 7 8 9 10-1.2
-0.8
-0.4
0
0.4
0.8
1.2- b -
Time (s)
a9
75
Fig. 4. 7 Cyclic values of the fault indicator mPa9, resulting from the 9th wavelet decomposition level
of the signals Isl under healthy and rotor bar broken (red and blue) during the tracking of (1-2s)f
component
Fig. 4. 8 Cyclic values of the fault indicator mPa9, resulting from the 9th wavelet decomposition level
of the signals Isl under healthy and rotor bar broken (red and blue) during the tracking of (1+2s)f
component
0 10 20 30 40 50 60 70 800
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
TIN
mP
a9
Healthy Broken bar
0 10 20 30 40 50 60 70 800
0.05
0.1
0.125
TIN
mP
a9
Healthy Broken bar
76
4.3 Analysis of rotor fault in double cage induction machine
Successful detection of outer cage faults in DCIMs requires understanding
similarities and differences with single cage broken bars phenomenon. The main
similarity between these two classes of motors in case of rotor fault is the existence of
interbar currents [1]-[5], and the chain of fault harmonics that appears in stator line-
currents [6]-[8].
For large or double squirrel cage motors, as long as the contact impedance between
the rotor bars and iron core is small or the copper bars are directly inserted into the
laminated iron slots, the broken bars are no longer a physical condition ensuring an open
circuit, since inter-bar or cross path currents can flow. If the resistance between the bars
and the iron core is low, currents will start to flow between the bars through the
lamination, which increases the stray-load losses in the machine and affect the torque
during the start-up [3]-[4]. Subsequently, these currents interact with the radial
component of the air-gap magnetic field, and compensate the rotor asymmetry caused
by rotor bar breakage and leads to axial vibrations [1],[4] and to temperature increase
[9]. In DCIMs these interactions can reduce significantly the amplitudes of rotor fault
components.
Another typical behavior of induction motors with rotor broken bars is the existence of
sideband components in the line currents at frequencies (12s)f whose amplitudes are
usually monitored for rotor diagnostic. The main difference between DCIMs and single
cage motors in case of broken bars is related to the inherent structure of the double cages
[10]. Double cage motors have two squirrel cages shorted with a common end ring or
with separate end rings. The schematic and the electrical equivalent circuit of the double
cage rotor are shown in Fig. 4.9. The outer cage is usually composed of small high
resistivity material bars, while the inner cage is made of larger, low-resistance bars [11].
The iron between the outer cage and the inner cage, together with the proximity of the
outer cage with the stator windings, causes the outer cage leakage reactance to be low.
Conversely, the leakage inductance of the inner cage is large since the magnetic
reluctance of flux path closing through the inner bar is low (Fig. 4.9).
Therefore, the rotor current is mainly confined to the high resistance outer cage at high
slip (i.e., startup) due to the dominance of the leakage inductance, thus obtaining high
startup torque. When steady state operation is reached, the leakage inductance is
negligible (low slip) and the outer cage resistance is dominant, which causes the current
to flow mainly in the low resistance inner cage. The rotor operates as a normal low-
resistance rotor, and the sensitivity of detecting the rotor fault from stator current is
significantly reduced. Considering that the depth of flux penetration into the rotor is
inversely proportional to the square root of the rotor frequency, the inner cage can be
nearly disregarded during the startup or during any abrupt slip increase due to load
transients.
77
Fig. 4. 9 Electrical equivalent circuit representation of a double squirrel cage induction motor
The sensitivity of MCSA has been experimentally evaluated in [7], [12] for single cage
and double cage rotor machines. It can be seen in Fig. 4.10 that the sensitivity of MCSA
for outer cage damage in double cage rotors under rated load is significantly lower than
that of the single cage rotor under identical conditions. The fl component is relatively
lower by 18 ~ 22dB for the double cage design, which corresponds to a decrease in
sensitivity by a factor of 10. The situation is worse for time-varying loads since the fault
components spread out resulting in lower peak magnitude. Considering that the default
fault alarm level for broken bars is set at -45~-35dB in commercial MCSA products (to
avoid false alarms) [12]-[13], outer cage faults of double cage motors are unlikely to be
detected unless a method dedicated to double cage motors is used.
Fig. 4. 10 Experimental measurements of broken bar component, frffc, with on-line MCSA under rated load for 0-3/44 broken bars for (left) single cage deep bar Al die cast rotor; (right) double cage
fabricated brass-Cu separate end ring rotor [7]
78
4.3.1 Motor Current Signature Analysis
4.3.1.1 System description
Experimental verification of the proposed method was performed on a 380V, 7.5 Hp,
12 A induction motor with a custom-made double cage rotor. A fabricated copper
separate end ring double cage rotor, shown in Fig. 4.11, was constructed to fit the stator
of an aluminum die cast induction motor, already available. The outer cage was made of
brass, which is common in large motors for obtaining high starting torque. The custom-
made rotor is designed and built so that it allows testing of the proposed method on a
motor representative of large motors.
The tests were performed for the healthy rotor and a faulty rotor after cutting 3 of 44
rotor bars at the bar end ring joint. The MCSA results shown for the double cage rotor in
Fig. 4.10 are obtained with the same test rotor. The motor load was controlled by
adjusting the field voltage of a 30 Hp DC generator coupled to the motor. Commercial
current sensors and a 16 bit DAQ board were used to measure the stator-line current isa
(the sampling frequency fs was 960 Hz) over a data acquisition window of 10 seconds
under load transient conditions from 10% to 90% of the full load. The second series of
tests was carried out during an acquisition time interval of 25 seconds under a load
profile from 10% to 50% then to 90% of the full load.
(a) (b)
Fig. 4. 11 Custom designed fabricated copper separate end ring double cage rotor sample with brass outer cage and copper inner cage(a), and the corresponding rotor lamination (b)
4.3.1.2 Results
4.3.1.2.1 Rotor Fault detection
A six level decomposition (n=6) was chosen to cover the frequency bands of the fault
79
components, as shown in Table 4.2. The proposed diagnosis approach was applied to the
stator current with lslf =52.10 Hz and then with r
slf =60.39 Hz, to isolate the contribution
of the fault components fl and fr, respectively. The first series of tests were conducted
under a large speed transient during 10 seconds, as reported by the speed profiles in
Figs. 4.12-a and 4.13-a, for healthy rotor and for three rotor outer cage broken bars,
respectively. The corresponding stator currents are shown in Figs. 4.12-b and 4.13-b.
The sixth-level approximation signals resulting from the DWT of )(ti lsl in healthy and
faulty conditions, computed under the assumption of a sliding frequency lslf =52.10Hz,
are depicted in Figs. 4.12-c and 4.13-c respectively.
Table. 4. 2 Frequency bands of approximation and detail signals
Approximation
signal, aj
Frequency
bands (Hz) Detail Signal, dj
Frequency
bands (Hz)
a6 [0 – 7.5] d6 [7.5 – 15]
a5 [0 – 15] d5 [15 – 30]
a4 [0 – 30] d4 [30 – 60]
In healthy condition, it can be observed that the approximation signal a6 (Fig. 4.12-c)
does not show any variation. This fact indicates that the fault component fl is absent in
the stator current (Fig. 4.12-b), which leads to the diagnosis of “healthy” condition of
the DCIM.
On the contrary, a significant variation in the amplitude of the approximation signal a6
can be observed under a fault condition with three broken outer cage bars, as shown in
Fig. 4.13-c. In steady state, under light load conditions (10% rated load), important
variations in la6 cannot be observed between 0~4 s. This is due to the fact that fault
components with small magnitude, superimposed on the fundamental, are not detectable
under light load conditions. However, during the deceleration transient due to the load
variation around t≈4s, an escalation in the magnitude of la6 proportional to the rate of
deceleration can be observed, as shown in Fig. 4.13-c.
The increase in the 6th approximation signal can be observed until reaching a quasi
steady-state magnitude at 90% rated load. The oscillations observed in the signal la6
with quasi-constant amplitude are the consequence of the time evolution of the
component fl issued from the stator current (Fig. 4.13-b) during the speed transient.
The second rotor fault signature tracked is related to the right sideband component at
frequency fr.
The corresponding experimental results, under healthy and three broken outer cage bars
are presented in Figs. 4.12-d and 4.13-d, respectively.
80
The observations for ra6 are similar to those of la6 . The variation of the 6th approximation
signal is negligible under healthy (Fig.4.12-d) condition, whereas a remarkable
evolution over time can be observed for the faulty case (Fig. 4.13-d). Analyzing the
approximation signals la6 and ra6 depicted in Figs. 4.13-c,d, one can note that the rotor
fault signature issued from the fault component related to fl shows larger variation than
that related to fr. This is due mainly to the damping effect of the machine-load inertia. In
any case, for reliable diagnosis, the diagnostic index is based on the sum of both
amplitudes.
In order to determine the threshold for the fault indicator Find, a second series of
experimental tests were conducted under healthy and faulty cases, with the time varying
load (speed) profile shown in Figs. 4.14 and 4.15. The load was increased from 10% to
50% and then to 90% within a 25s interval. The results are similar to those Figs. 4.12
and 4.13.
Fig. 4. 12 DWT analysis of stator current under transient operating condition (10%-90% rated
load):a) speed profile, b) phase current, c) fl component, and d) fr component under healthy
conditions
0 2 4 6 8 10
1740
1800
Sp
eed
(rp
m)
a0 2 4 6 8 10
-20
0
20
isa (
A)
0 2 4 6 8 10-0.4
0
0.4
al6
0 2 4 6 8 10-0.4
0
0.4
Time (s)
ar6
a)
b)
c)
d)
81
Fig. 4. 13 DWT analysis of stator current under transient operating condition (10%-90% rated
load):a) speed profile, b) phase current, c) fl component, and d) fr componentwith3 broken outer
cage bars
Fig. 4. 14 DWT analysis of stator current under transient operating condition (10%-50%-90%
rated load): a) speed profile, b) phase current, c) fl component, and d) fr component under
healthy conditions
0 2 4 6 8 10
1740
1800
Sp
eed
(rp
m)
a0 2 4 6 8 10
-20
0
20is
a (
A)
0 2 4 6 8 10-0.4
0
0.4
al6
0 2 4 6 8 10-0.4
0
0.4
Time (s)
ar6
a)
b)
c)
d)
0 5 10 15 20 25
1740
1800
Sp
eed
(rp
m)
a)
d)
b
b)
c)
0 5 10 15 20 25-20
0
20
isa
(A
)
0 5 10 15 20 25-0.4
0
0.4
al6
0 5 10 15 20 25-0.4
0
0.4
Time (s)
ar6
82
Fig. 4. 15 DWT analysis of stator current under transient operating condition (10%-50%-
90% rated load):a) speed profile, b) phase current, c) fl component, and d) fr component
with3 broken outer cage bars
4.3.1.2.2 Fault quantification
Once the state of the machine has been qualitatively diagnosed, a quantitative
evaluation of the fault severity is necessary. The fault indicator is periodically
calculated, every 400 samples, by using a window of 6400 samples (δx=400 samples,
x=6400 samples). The values of δx and x were chosen according to the desired time
sensitivity to observe the fault evolution.
The periodic calculation of the normalized fault indicator corresponding to the behavior
of the healthy and faulty motors reported in Figs. 4.14 and 4.15, is depicted in Fig. 4.16.
After repeating a number of tests, the fault indicator for the faulty case can be
considered as a baseline for setting the threshold to discriminate healthy from faulty
rotors with broken outer cage bar condition, as shown in Fig. 4.16.
The indicator Find which is proportional to the sum of la6 and ra6 , shows significant
increase under faulty conditions. The large energy deviation observed in faulty
conditions under the load transient verifies the effectiveness of the proposed approach.
The fault indictor under healthy conditions is always lower than that of the faulty case
even under load transients, as can be seen in Fig. 4.16. The experimental results of Figs.
4.12-4.15 clearly show the main advantage of the proposed method: the outer cage faults
in double cage motors can be reliably observed with high sensitivity even under time-
0 5 10 15 20 25
1740
1800
Sp
eed
(rp
m)
a)
d)
b
b)
c)
0 5 10 15 20 25-20
0
20is
a (
A)
0 5 10 15 20 25-0.4
0
0.4
al6
0 5 10 15 20 25-0.4
0
0.4
Time (s)
ar6
83
varying load transients as the assessment is not disturbed for a healthy machine under
load transients.
Fig. 4. 16 Values of the fault indicators: normalized Find (Black line)resulting from the 6th
wavelet decomposition level of the stator current under healthy and faulty (3 broken outer
cage bars) conditions with speed-varying conditions. Left side component (Blue line), and
right side component (Red line)
4.3.2 Motor Vibration Signature Analysis
In healthy conditions only the fundamental frequency f exists in stator currents of a
double cage induction machine. If the rotor part is damaged, the rotor symmetry of the
machine is lost producing a reverse rotating magnetic field related to an inverse
sequence component at frequency −sf. This inverse sequence is reflected on the stator
side, producing the frequency (1−2s)f. These frequency components generate
electromagnetic and mechanical interactions between stator and rotor parts.
Consequently torque and speed ripple effects are generated at frequency 2sf, which
modulate the rotating magnetic flux [6].
This modulation produces two current components, i.e., an additional left-side
component at (1−2s)f and a right side component at (1+2s)f. Following this interaction
process, the frequency content of the stator currents show series of fault components at
the following frequencies ((1±2ks)f)k=1,2,3,…). More specifically, for large or double
squirrel-cage motors, as long as the contact impedance between the rotor bars and iron
core is small or the copper bars are directly inserted into the laminated iron slots, the
broken bar is no longer a physical condition ensuring an open circuit and inter bar or
cross-path currents can flow. As a consequence, these inter bar transverse currents
interact with the radial stator flux density, generating axial forces. These facts lead
mainly to the presence of a first chain of fault frequency components at
(fmec±2ksf)k=1,2,3,…, and a second one at ((6-2ks)f)k=1,2,3,…, in radial and axial vibration
0 10 20 30 40 50 6010
-4
10-3
10-2
10-1
100
101
TIN
[%]
mPa6l (3outer cage BRB)
mPa6r (healthy)
mPa6r (3outer cage BRB)
mPa6l (healthy)
Find
(healthy)
Find
(3outer cage BRB)Threshold for 3outer cage BRB detection
84
directions (fmec denotes the mechanical speed of the motor) [15]- [18]. In the following,
the focus will be exclusively on tracking the most relevant fault components of the
harmonic chains((6-2ks)f)k=1,2,3,… and (fmec±2ksf)k=1,2,3,…, issued from axial vibrations.
4.3.2.1 System description
In order to evaluate the performances of the proposed approach, two double cage
induction motors are available; one healthy, and the second with a drilled broken bar
(the bar was completely disconnected from the common end-ring). The characteristics of
the double cage induction motors used for experiments are presented in Table 4.3. A
three-phase autotransformer of 30 kVA, 0-380 V is used as motor regulated supply. A
four quadrants 7,83 kW dc electrical drive is adopted to reach the different planned load
conditions. One piezoelectric accelerometers Brüel & Kjær model 4507 B 005, was
mounted for measuring axial vibrations of the core motors. Fig. 4.17 shows detailed
photos of the healthy and drilled rotor (left), and details of the test-bed (right). In Fig.
4.18 and Fig. 4.19 instantaneous values of rotor speed and axial vibration signals are
depicted for healthy and faulty conditions respectively. All signals reported have been
recorded during 20 seconds. The tests were carried out considering a speed transient
from 0% to 70% of full load.
Table. 4. 3 Data of the double rotor cage motor
Data Value
Rated Power kW 5.5
Rated stator voltage V 400
Rated current A 13
Rated frequency Hz 50
Rated speed rpm 2870
Rotor diameter mm 110
Axial length of the rotor mm 90
Air gap length mm 0.5
Number of stator slots 36
Number of rotor slots 30
Fig. 4. 17 Photos of the healthy and drilled broken bar (left), and details of the test-bed (right)
85
Fig. 4. 18 Instantaneous values of speed (a), and axial vibration signal (b) under healthy
conditions
Fig. 4. 19 Instantaneous values of speed (a), and axial vibration signal (b) under broken bar
4.3.2.2 Results
4.3.2.2.1 Rotor Fault detection
With a sampling frequency fs=2.0kHz, a six level decomposition (J=6) was chosen in
order to cover the frequency bands in which we can track the contribution of the first
chain of harmonic ((6-2ks)f)k=1,2,3,…. The second chain of fault component
0 2 4 6 8 10 12 14 16 18 202850
2900
2950
3000
3050- a -
Time (s)
Sp
eed
(rp
m)
0 2 4 6 8 10 12 14 16 18 20-1
-0.5
0
0.5
1- b -
Time (s)
Accele
rati
on
(m
/s2)
0 2 4 6 8 10 12 14 16 18 202850
2900
2950
3000
3050- a -
Time (s)
Sp
ee
d (
rp
m)
0 2 4 6 8 10 12 14 16 18 20-1
-0.5
0
0.5
1- b -
Time (s)
Accele
rati
on
(m
/s2)
86
(fmec±2ksf)k=1,2,3,…, will be tracked in a frequency band corresponding to seven level
decomposition (J=6). The frequency band repartition corresponding to the above
decompositions are detailed in Table. 4.4. The chains of fault components ((6-
2ks)f)k=1,2,3,… and (fmec±2ksf)k=1,2,3,…, will be tracked in the frequency bands [0: 15.625]
and [0: 7.812] respectively, after appropriate frequency sliding applied to axial vibration
signals. All signals reported have been recorded during 10 seconds.
Table. 4. 4 Frequency bands at each level of decomposition
In this chapter, the proposed diagnosis technique is extended to faults detection in
Multiphase electrical machines. Multiphase Permanent-Magnet Generators are an
attractive alternative to induction machines for a variety of applications owing to their
reliability and dynamic performance, suited for emerging applications such as
automotive or traction systems. In this context, diagnosing the status of the rotor
magnets is crucial for improving the reliability of the generators. This Chapter is
firstly focused on the demagnetization of the rotor magnet trailing edges, due to large
stator currents, in five-phase surface-mounted permanent magnet synchronous
generators under Time-varying conditions. Consequently, the classical application of
Fourier analysis for processing the back-emf induced in the α-β planes fails as the fault
components intended to be monitored to assess the magnets status are spread in a
bandwidth proportional to the speed variation. In this context, the back-emf induced in
the α-β planes is analyzed by the proposed diagnosis technique for the detection of
rotor demagnetization in multiphase surface-mounted permanent magnet generator
under speed-varying conditions. The proposed methodology is validated by means of
two dimensional (2-D) Finite Element Analysis (FEA) and numerical simulations.
Moreover, a cyclic quantification of the fault extent over time was introduced for
accurate rotor fault detection.
The second subpart of this section investigates the behavior of multiphase induction
machines with an odd number of phases in investigated under the assumption that the
stator winding is unbalanced owing to a fault or an incipient damage. The analysis
leads to a method to assess the unbalance condition of the machine, based on the
calculation of the space vectors of the stator currents in the available α-β planes.
Experimental results for the analysis established in time and frequency domains show
interesting results to be extended to time-frequency domain.
5.2 Characterization of Rotor Demagnetization in Five-Phase
Surface–Mounted Permanent Magnet Generator
5.2.1 System description
The numerical modeling of the used five-phase surface-mounted PMSG is developed for healthy and local magnet demagnetization conditions. Multiple space vector theory is considered to represent the five-phase system by two space vectors and a zero- sequence component as detailed in Appendix.2. Under the assumptions usually adopted for the analysis of ac machines, the magnetic field produced by the stator windings in the air gap can be expressed in a stator reference frame in terms of stator current space vectors in the following compact form:
96
3 7 9* *3 7 91 1 3 3 1
5,
2 3 7 9S S S Sj j j jS wS wS wS
S S e wS S S S S
N K K Kh t K i e i e i e i e
p
(5. 1)
where, NS is the number of series-connected conductors per phase, is the air gap
length, p the number of pairs of poles, e the real part operator, KwS the -th winding
coefficient, S a stationary angular coordinate in electrical radians whose origin is
aligned with the magnetic axis of phase 1, whereas 1Si and 3Si are the stator current
space vectors.
The symbol “*” identifies the complex conjugate quantities. Besides the fundamental
component, (5.1) takes into account the third, the seventh and the ninth spatial
harmonics, and is expressed in terms of the instantaneous values of the stator current
vectors. It is worth noting that the fifth spatial harmonic is null, since it can be
generated only by the zero-sequence component of the stator currents, which is zero
owing to the star connection of the windings.
With the usually adopted control strategy for PMSGs, the air gap distribution of the
stator MMF is maximum along the quadrature axis. In this way, one half of each
magnet is reverse magnetized. This can lead to a local demagnetization of the rotor
magnets, which is reproduced by simply removing part of the magnetic material from
the trailing edge.
The magnetic field produced by the rotor magnets in the air gap, in a rotor reference
frame, can be written as:
3 53 53 5
7 97 97 9
2,
1 1
3 5
1 1
7 9
R
R R
R R
j jjMR R e
j jj jj j
j jj jj j
Hh t e e e
e e e e e e
e e e e e e
(5. 2)
where, R is an angular coordinate in electrical radians in the rotor reference frame, -
2 is the pole arc of the surface-mounted permanent magnets, and identifies the
demagnetized portion of the magnets (Fig. 5.1).
By neglecting the slot opening effect, and assuming a unitary relative recoil
permeability of the magnets, the value of HM can be expressed as:
0
M RM
BH
, (5. 3)
where, M is the magnet thickness, and BR is the residual flux density of the magnet
material.
97
m
R
Stator
Rotor
Fig. 5. 1 Schematic draw of a pair of surface-mounted permanent magnets in
healthy and fault conditions
Besides the fundamental component, (5.2) takes into account the third, the fifth, the
seventh and the ninth spatial harmonics. Fig. 5.2 shows the amplitude variation of
every single spatial harmonic in the flux density distribution as a function of the pole
arc reduction in electrical radians for the considered machine (Table.5.1).
Table. 5. 1 Five-Phase PMSG Parameters (FEA)
Rated torque 12 Nm
Torque over current ratio 2.4 Nm/A
Rated speed 3000 rpm
Phase resistance 0.55 Ohm
Phase reactance (100 Hz) 4.5 Ohm
Pole number 4
Stator inner radius 40 mm
Stator outer radius 68 mm
Stack length 100 mm
Slot number 40
Slot opening width 1.8 mm
Slot opening depth 0.5 mm
Stator winding pitch 9/10
Radius of the rotor surface 36 mm
Magnet-arc to pole-pitch ratio 77.14 / 90
Magnet radial thickness 3 mm
Magnet remanence 1.3 T
Relative recoil permeability 1.13
Magnetization type Radial
98
The amplitudes are normalized by the amplitude of the fundamental. It is a matter of
fact that a reduction of the pole arc leads to a variation of the harmonic content in the
flux linkage, and thus in the back-emf. In the present work, and as it is detailed below,
the focus is exclusively on tracking the contribution of the ninth and seventh inverse
harmonics issued from the back-emf.
To evaluate the stator linkage fluxes, it is necessary to consider the contributions of
the air gap magnetic field and of the leakage fluxes. The air gap magnetic field
contribution can be derived by means of (5.1) and (5.2).
Fig. 5. 2 Harmonic amplitude variation in the flux density distribution as a function of the
magnet pole arc reduction in electrical radians
The contribution of the leakage fluxes can be easily described by introducing two
leakage inductances (the leakage inductances LSd1 and LSd3 for the - and -
planes, respectively).
In conclusion, the mathematical model of the surface-mounted PMSG, written in terms of multiple space vectors, can be written as follows:
00
SS
dv
dt
, (5. 4)
11 1
SS S S
dv R i
dt
, (5. 5)
33 3
SS S S
dv R i
dt
, (5. 6)
0 1 20.26170
0.2
0.4
0.6
0.8
1
Magnet pole arc reduction (rad)
No
rmalized
Harm
on
ic A
mp
litu
des
1st Harmonic
3rd Harmonic
5th Harmonic
7th Harmonic
9th Harmonic
Reduced pole arc
99
where the zero-sequence and the - and -space vectors of the linkage fluxes are given by
50 5
jS e M e , (5. 7)
91 1 1 1 9
j jS S S M ML i e e , (5. 8)
3 73 3 3 3 7
j jS S S M ML i e e . (5. 9)
In (5.7)-(5.9), is the rotor position in electrical radians, whereas LS1 and LS3 are the
- and -synchronous inductances, which can be expressed as
22 9
1 1 181
wSS Sd SS wS
KL L L K
, (5. 10)
2 23 7
3 39 49wS wS
S Sd SS
K KL L L
, (5. 11)
where
20
2
5
2S
SS
L NL
p
, (5. 12)
and is the pole pitch.
The space vectors of the fluxes linked with the stator windings due to the permanent
magnet field harmonics, can be expressed as follows:
1 1
j jm M wSK e e (5. 13)
3 333
9
j jwSm M
Ke e
(5. 14)
7 777
49
j jwSm M
Ke e
(5. 15)
9 999
81
j jwSm M
Ke e
(5. 16)
where
02
2 S MM
L N H
(5. 17)
The electromagnetic torque Tem assumes the following form:
,1 ,3 ,7 ,9em em em em emT T T T T (5. 18)
where
100
,1 1 1
5
2
j j jem wS M ST p K i j e e e
(5. 19)
3 3 33,3 3
5
2 3
j j jwSem M S
KT p i j e e e
(5. 20)
7* 7 77,7 3
5
2 7
j j jwSem M S
KT p i j e e e
(5. 21)
9* 9 99,9 1
5
2 9
j j jwSem M S
KT p i j e e e
(5. 22)
As can be seen, four torque contributions are present, each one identified by the order
of the related spatial harmonic in the air gap.
Contributions Tem,1 and Tem,3 can be ripple free owing to the synchronization of 1Si with je , and 3Si with 3je . On the contrary, contributions Tem,7 and Tem,9 are oscillating,
because *3Si is not synchronized with 7je , as well as *
1Si is not synchronized with 9je .
Note that the stator current space vector 3Si is usually kept equal to zero by the control
system in a standard five-phase drive. A non-zero value of 3Si is used only in high
torque density motor drives, as discussed in [1]-[4]. In the present investigation, a null
value of 3Si is assumed. Consequently, only the contribution Tem,9 has to be minimized
in order to reduce the torque ripple. This goal can be obtained either by an opportune
choice of the permanent magnet pole arc or by suitable short-pitch stator windings.
Taking into account (5.5), (5.6), (5.8), (5.9), (5.13), (5.14), (5.16) and (5.17), the space
vectors 1Se and 3Se of the back-emf, can be expressed as shown in (5.23) and (5.24),
which emphasize the low order harmonic content of the back-emf space vectors.
21 1
999 2
2 cos2
2 9cos 9
9 2
jj
S M wS
jjM wS
e j K e e
j Ke e
(5. 23)
333 2
3
777 2
2 3cos 3
3 2
2 7cos 7
7 2
jjM wS
S
jjM wS
j Ke e e
j Ke e
(5. 24)
In order to validate the theoretical analysis of the emf harmonic content under speed
varying-conditions, the simulation of a five-phase surface-mounted PMSG has been
carried out using FEA. The parameters of the generator are summarized in Table 5.1.
A double-layer stator winding, having two slots per pole and per phase, with 9/10 coil
pitch, is considered (KwS9 = 0.024). The pole arc for the surface-mounted permanent
magnet has been reduced of one seventh in respect to the polar pitch in order to
eliminate the seventh harmonic in the resulting emf. The cross-section of the five-
phase PMSG, with a superimposed flux plot obtained by FEA, in healthy no-load
101
conditions, is shown in Fig. 5.3.
The simulations have been performed in no-load conditions under speed varying
conditions (from 1500rpm to 3000rpm), firstly with healthy magnets ( = 0°) and,
then, with magnets having a reduced pole arc ( = 15°) in order to reproduce a
demagnetization on the trailing edges. By means of the FEA simulations, the linkage
fluxes with the five stator phases have been determined as function of the rotor
position. For the analysis of the sensitivity to the fault, the emfs have been divided by
the rotor speed (expressed in electrical radians) obtaining the so called ‘normalized
emf’.
Fig. 5. 3 Cross-section of the five-phase PMSG, with a superimposed flux plot obtained by FEA,
in healthy no-load conditions.
The large speed transient profile adopted during the simulations under healthy and faulty
conditions is depicted in Fig. 5.4-a. The corresponding back-emfs under faulty
conditions are depicted in Fig. 5.4-b. All signals reported have been recorded during 15
seconds, with a sampling frequency of 3.2 kHz.
102
Fig. 5. 4 Instantaneous values of the electrical speed (a), and the corresponding back-emfs under
faulty conditions
5.2.2 Results
With reference to the machine whose parameters are reported in Table 5.1, the
sampling frequency fs is chosen equal to 3.2kHz and a three-level decomposition (J=3)
is adopted to cover the frequency bands in which the frequency component
characteristics of the fault can be tracked (see Table 5.2).
As explained in Section III, the contribution of 7th inverse harmonic component of the
normalized back-emf space vector /3Se can be observed in the approximation signal a3
after appropriate sliding frequency. In order to isolate the contribution of the 7th inverse
harmonic fault component in the frequency band of the approximation signal a3, a
sliding frequency fsl = -(7fS+12.5 Hz) was chosen to shift the α3-β3 components of the
normalized back-emfs under healthy and faulty conditions. As already explained, the
sliding frequency is chosen in such a way that the expected fault harmonic is shifted in
the middle of the frequency band of the approximation signal a3. The results of this
analysis are shown in Figs. 5.5-5.6. The wavelet decomposition obtained when the
machine is healthy should be compared with the one obtained in the case of faulty rotor.
The absence of amplitude variations in a3 (Fig. 5.5-b) is due to the low contribution of
the 7th harmonic in healthy conditions, which allows one to diagnose the healthy state of
the machine. By contrast, under a local demagnetization (Fig. 5.6-b) , it is possible to
notice an amplitude increase in the approximation signal a3, in comparison to the
healthy case (Fig. 5.5-b). This result means a clear detection of rotor demagnetization.
0 5 10 15
150
200
250
300
350
Time (s)
Ele
ctr
ical sp
eed
(ra
d/s
)
0 5 10 15-100
-50
0
50
100
Time (s)
[ V
. ]
back-emf1
back-emf2
back-emf3
back-emf4
back-emf5
10 10.005 10.01-100
-50
0
50
100
103
Table. 5. 2 Frequency band of each level
Approximations
«aj »
Frequency
bands (Hz)
Details
« dj »
Frequency
bands (Hz)
a3 : [0 – 200] d3 : [200 – 400]
a2 : [0 – 400] d2 : [400 – 800]
a1 : [0 – 800] d1 : [800– 1600]
Fig. 5. 5 Instantaneous values of the electrical speed (a), and the third approximation signal (a3)
issued from Wavelet analysis of the α3-β3 components of the back-emf space vector under healthy
conditions.
Fig. 5. 6 Instantaneous values of the electrical speed (a), and the third approximation signal (a3)
issued from Wavelet analysis of the α3-β3 components of the back-emf space vector under local
rotor magnet demagnetization conditions.
0 5 10 15
150
200
250
300
350
Time (s)
Ele
ctr
ica
l S
pe
ed
[ra
d/s
]
- a -
0 5 10 15
-5
0
5
Time (s)
a3
- b -
0 5 10 15
150
200
250
300
350
Time (s)
Ele
ctr
ical S
peed
[ra
d/s
]
- a -
0 5 10 15
-5
0
5
Time (s)
a3
- b -
104
Once the state of the machine has been qualitatively diagnosed, a quantitative evaluation
of the fault severity is necessary. The fault indicator is periodically calculated, every 400
samples, by using a window of 6400 samples (δx=400 samples, x=6400 samples). The
values of δx and x were chosen according to the desired time sensitivity to observe the
fault evolution. Fig. 5.7 shows the shapes of the corresponding fault indicators in faulty
and healthy conditions respectively. These results mean that the proposed methodology
leads to a clear detection of rotor demagnetization.
Fig. 5. 7 Values of the fault indicator mPa3 (eS3), corresponding to the 7th inverse harmonic component, resulting from the approximation signal a3 under large speed transient, for healthy
and local rotor demagnetization (15°) conditions.
5.3 Characterization of stator fault in seven-phase induction
machine
Multiphase drives are receiving an increasing attention by the research community in high power applications. In this section, the behavior of seven-phase induction machine is investigated under incipient stator unbalance. The analysis leads to a method to assess the unbalance condition of the machine, based on the calculation of
the space vectors of the stator currents in the available - planes. The analytical model of a multiphase induction motor with unbalanced stator winding is completely developed in [5] . The investigation of the current stator space vectors in the available
- planes has shown interesting results for stator fault detection and localization. Results are confirmed by experimental tests.
0 20 40 60 80 100 1200
2
4
6
8
10
12
TIN
mP
a3
Demagnetized magnets (15°)
Healthy
105
5.3.1 System description
Multiphase machines are usually fed by a multiphase inverter, whose command signals are calculated by a control system within a closed-loop scheme. Nevertheless it is of some interest to analyze the behavior of machine under the assumption that the control scheme is an open loop, such as the constant V/Hz control scheme. The main reason is that the understanding of such control schemes is the starting point for more complex cases.
A complete drive system has been built and some experimental tests have been realized. The experimental set-up consists of a 7-phase IGBT inverter and a 4 kW, 7-phase, 4-pole squirrel cage induction motor. The parameters of the motors are shown in Table 5.3. A schematic diagram and some pictures of the experimental set-up are shown in Fig. 5.8. The control algorithm is very simple, without any form of compensation of the voltage drop on the stator impedance.
All the tests have been carried out by feeding the motor with 80 V at 25 Hz. The resulting motor speed in healthy conditions is around 700 rpm, and the load has been adjusted so that the torque produced by the motor is 15 Nm, i.e., about two third of the rated torque.
During the experimental tests, an extern resistor has been added in series with the machine phases to reproduce a fault condition in a non-destructive way.
Table. 5. 3 Parameters of the Seven-Phase Machine
Trated = 24 Nm LS1 = 180 mH
Is,max = 7.5 A(peak) LR1 = 180 mH
IS1d,rated = 3.6 A(peak) M1 = 175 mH
frated = 50 Hz LS3 = 24 mH
RS = 1.3 LR3 = 24 mH
RR1 = 1.0 M3 = 19 mH
RR3 = 0.8 LS5 = 10 mH
RR5 = 0.6 LR5 = 10 mH
p = 2 M5 = 7mH
Laboratory controllable 3-ph
AC source (50 Hz) DC-link voltage
3-P Rectifier
…
7 Phases
7-P IM LOAD
…
Stator currents
(6 sensors)
7 PWM leg signals
Control system (DSP TI -TMS320F2812)
7-P Inverter dc-link
Additional resistance
Speed and torque sensors
a)
106
b) c)
Fig. 5. 8 Experimental set-up. a) Schematic diagram of the test bench and position of the current
and voltage sensors. b) Seven phase induction machine. c) Seven phase inverter
5.3.2 Results
Without additional resistance, the behavior of the machine is regular and the stator
currents are practically sinusoidal.
Figs. 5.9-5.10 show the behavior of 3Si and 5Si in these operating conditions. As can be
seen in Figs. 5.9-a and 5.10-a, 3Si and 5Si are noisy quantities even in healthy operating
conditions. The reason is the current ripple due to the pulse width modulation.
In addition, the control scheme adopted for the experimental tests is of open-loop type.
Consequently, the currents are affected by the inverter nonlinearity (dead times,
voltage drop of the conducting switches).
Finally, some manufacturing inaccuracies may lead to small asymmetries of the motor
windings. As a result, 3Si and 5Si cannot be exactly null.
Fig. 5.9-b and 5.10-b show that spectra of 3Si and 5Si . It can be noted that the most
important harmonic component of 3Si is at 75 Hz, i.e., three times the fundamental
frequency. This fact suggests that the currents in the planes 3-3 and 5-5 are mainly
due to the perturbations resulting from the manufacturing machine asymmetry and the
inverter nonlinearity.
It is straightforward to extract the harmonic components of 3Si and 5Si at 25 Hz. The
behavior of these components is shown in Fig. 5.9-c and 5.10-c. As predicted by the
theoretical analysis [5], the current space vectors move on elliptical trajectories, and
the amplitudes of the major axes are lower than 50mA.
The behavior of the drive has been assessed under a phase imbalance. Figs. 5.11 and
5.12 show the behavior of the drive when an additional resistance, equal to twice the
stator resistance, is added to phase 1, whereas Fig. 5.13 and 5.14 show the behavior of
the drive when the additional resistance is added to phase 3.
As can be seen, the behavior of the drive is now very different from that in healthy
condition.
107
The magnitudes of 3Si and 5Si are now sensibly greater and can be easily detected.
Their spectra confirm that the most important harmonic components are at 25 Hz, in
perfect agreement with the theoretical analysis.
When the fault is in phase 1, the directions of the major axes of the ellipses in Fig.
5.11-c and 5.12-c coincide with that of the -axis, as expected.
When the fault is in phase 3, the major axis of the ellipse of Fig. 5.11-c forms an angle
of -50 degrees with the -axis (an angle of -51.42 degrees was expected), whereas the
major axis of the ellipse of Fig. 5.14-c forms an angle of 158 degrees (an angle of 154
degrees was expected). As can be seen from these results, there is a good agreement
between theoretical predictions and experimental tests. Actual investigations are in
progress for extending the developed technique based on time and frequency domain
informations to time-frequency domain using the diagnosis technique validated in this
thesis.
Component (A)
Com
ponen
t
(A
)
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5
Frequency (Hz)
Am
pli
tud
e (A
)
-100 -50 0 50 100
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Component (A) C
ompo
nent
(
A)
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
a) b) c)
Fig. 5. 9 - Experimental result. Behavior of the drive in healthy condition. a) Behavior of 3Si . b)
Spectrum of 3Si . c) Trajectory of the components of 3Si at 25 Hz
Component (A)
Com
ponen
t
(A
)
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5
Frequency (Hz)
Am
pli
tud
e (A
)
-100 -50 0 50 1000
0.02
0.04
0.06
0.08
0.1
Component (A)
Com
pone
nt
(A
)
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
a) b) c)
Fig. 5. 10 Experimental result. Behavior of the drive in healthy condition. a) Behavior of 5Si . b)
Spectrum of 5Si . c) Trajectory of the components of 5Si at 25 Hz
108
Component (A)
Com
ponen
t
(A
)
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5
Frequency (Hz)
Am
pli
tude
(A)
-100 -50 0 50 100
0.1
0.2
0.3
0.4
0.5
0.6
Component (A)
Com
pone
nt
(A
)
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
a) b) c)
Fig. 5. 11 Experimental result. Behavior of the drive when an additional resistance is in
series with phase 1. a) Behavior of 3Si . b) Spectrum of 3Si . c) Trajectory of the
components of 3Si at 25 Hz.
Component (A)
Com
ponen
t
(A
)
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5
Frequency (Hz)
Am
pli
tud
e (A
)
-100 -50 0 50 100
0.1
0.2
0.3
0.4
0.5
Component (A)
Com
pone
nt
(A
)
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
a) b) c)
Fig. 5. 12 Experimental result. Behavior of the drive when an additional resistance
is in series with phase 1. a) Behavior of 5Si . b) Spectrum of 5Si . c) Trajectory of the
components of 5Si at 25 Hz.
Component (A)
Com
ponen
t
(A
)
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5
Frequency (Hz)
Am
pli
tud
e (A
)
-100 -50 0 50 100
0.1
0.2
0.3
0.4
0.5
Component (A)
Com
pone
nt
(A
)
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
a) b) c)
Fig. 5. 13 Experimental result. Behavior of the drive when an additional resistance is
in series with phase 1. a) Behavior of 3Si . b) Spectrum of 3Si . c) Trajectory of the
components of 3Si at 25 Hz
109
Component (A)
Com
ponen
t
(A
)
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5
Frequency (Hz)
Am
pli
tude
(A)
-100 -50 0 50 100
0.1
0.2
0.3
0.4
0.5
0.6
Component (A)
Com
pone
nt
(A
)
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
a) b) c)
Fig. 5. 14 Experimental result. Behavior of the drive when an additional resistance is
in series with phase 1. a) Behavior of 5Si . b) Spectrum of 5Si . c) Trajectory of the
components of 5Si at 25 Hz
5.4 Conclusion
The proposed diagnosis technique was extended to the detection of rotor demagnetization, in five-phase surface-mounted permanent magnet synchronous generators under time-varying conditions. The proposed methodology was validated by means of two dimensional (2-D) Finite Element Analysis (FEA) and numerical simulations. Moreover, a cyclic quantification of the fault extent over time was introduced for accurate rotor fault detection.
Another important issue of stator fault detection and localization in multiphase induction machines with an odd number of phases was experimentally investigated. The analysis leads to a method to assess the unbalance condition of the machine, based on the calculation of the space vectors of the stator currents in the available α-β planes. The issued results in time and frequency domains are under investigation to be extended to time-frequency domain.
110
REFERENCES
[1] L. Parsa, H. A. Toliyat, “Five-phase permanent-magnet motor drives,” IEEE
Trans. on Ind. Appl., Vol. 41, No. 1, Jan./Feb. 2005, pp. 30-37.
[2] L. Parsa, N. Kim, H. Toliyat, “Field weakening operation of a high torque
density five phase permanent magnet motor drive,” in Proc. of the IEEE-
IEMDC’05, 15-18 May 2005, pp. 1507 - 1512.
[3] L. Parsa, H. A. Toliyat, "Sensorless direct torque control of five-phase interior
permanent-magnet motor drives, " IEEE Trans. on Ind. Appl., Vol. 43, No. 4,
July/Aug. 2007.
[4] C. Olivieri, G. Fabri, M. Tursini, "Sensorless control of five-phase brushless dc
motors", SLED’10, 9-10 July 2010, Padova, Italy, pp. 24-31.
[5] L. Zarri, M. Mengoni, Y. Gritli, A. Tani, F. Filippetti, G. Serra, D. Casadei,
“Behavior of multiphase induction machines with unbalanced stator windings,”
Proc. of SDEMPED11, Bologna, Italy, Sept. 5-8, pp. 84-91.
111
112
CONCLUSIONS
In the current thesis, a new diagnosis technique for electrical machines operating in
time-varying conditions has been presented, where the validity under speed-varying
condition or fault-varying condition was experimentally validated.
After an exhaustive analysis of the potential failure modes in electrical machines, such
as stator and rotor electrical/mechanical faults, investigated in this thesis, a literature
review of the corresponding diagnosis techniques was firstly established leading to the
following possible improvements achieved by the proposed diagnosis technique in this
thesis:also presented leading .
1) Capability of monitoring the fault evolution continuously over time under any
transient operating condition;
2) No requirement for speed/slip measurement or estimation;
3) Higher accuracy in filtering frequency components around the fundamental;
4) Reduction in the likelihood of false indications by avoiding confusion with other
fault harmonics (the contribution of the most relevant fault frequency components
under speed-varying conditions are clamped in a single frequency band);
5) Low memory requirement due to low sampling frequency;
6) Reduction in the latency of time processing (no requirement of repeated sampling
operation).
The effectiveness of the proposed diagnosis technique was then experimentally
evaluated for the detection of rotor broken bars in single and then in double squirrel cage
induction motors under speed-varying conditions. Results issued from motor current
signature analysis and vibration signature analysis using the proposed technique have
shown high reliability fault indexes.
Finally, the detection of rotor demagnetization, in five-phase surface-mounted
permanent magnet synchronous generators under time-varying conditions was
investigated in the fifth chapter showing the high accuracy of detection for this
category of fault. An important issue of stator fault detection and localization in
multiphase induction machines with an odd number of phases was experimentally
investigated. The issued results in time and frequency domains are under investigation
to be extended to time-frequency domain using the developed technique.
Possible improvements of the presented technique can be by combining electrical and
mechanical signature analysis for improving the relevance of the fault index. This
issue can be also achieved by the use of AI techniques planned for future works.
113
114
APPENDIX. 1: WRIM MODEL
Representing motor variables in two different reference frames will make the impedance
matrix dependent on the rotor electrical angle. Anyway on the hypothesis of null
homopolar current component the equations number is reduced to six, i.e. four voltage
equations and two mechanicals. For the derivation of the mathematical model the
following assumptions are considered: infinite iron permeability, smooth air gap, and
three-phase symmetry of stator and rotor windings with sinusoidal distribution of the air